_FourierSeries

it.grypho.scala.leonardo.scalar._FourierSeries
case class _FourierSeries(e: _Expression, v: _Variable, period: _Expression, n: _Expression) extends _Functional

Truncated Fourier series of e in v over one period centred on zero: fourierSeries(e, v, period, n).

Like _Taylor, v is the expansion variable rather than a binder: it appears free in the result. It is kept out of children and carried through rebuild so substitute cannot rewrite the variable the expansion is taken in.

Unlike _Taylor, the coefficients are numeric: each is a definite integral evaluated by Simpson's rule, so period must reduce to a concrete positive number and the integrand must be evaluable over [-period/2, period/2]. Anything else leaves the node symbolic, the fixpoint convention shared with the transforms.

Not to be confused with transform._Fourier (fourier(e, t, w)), which is the Fourier transform -- a different operation with a different result type.

Value parameters

e

the expression to expand

n

the highest harmonic retained

period

the period, T

v

the expansion variable

Attributes

Graph
Supertypes
trait Serializable
trait Product
trait Equals
class _Functional
trait _Expression
class Object
trait Matchable
class Any
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Members list

Value members

Concrete methods

override def children: List[_Expression]

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Attributes

Definition Classes
override def eval(env: Environment): Either[_Expression, _Value]

Reduces this expression in the given environment.

Reduces this expression in the given environment.

Value parameters

env

variable bindings and display precision

Attributes

Returns

Right(v) when all free variables resolved to concrete values; Left(e) when reduction is partial or impossible

Definition Classes
override def rebuild(c: List[_Expression]): _Expression

Reconstructs the same node shape with replacement sub-expressions.

Reconstructs the same node shape with replacement sub-expressions.

Value parameters

newChildren

replacements in the same order and count as children

Attributes

Definition Classes
override def toString: String

Returns a string representation of the object.

Returns a string representation of the object.

The default representation is platform dependent.

Attributes

Returns

a string representation of the object.

Definition Classes
Any

Inherited methods

def productElementNames: Iterator[String]

Attributes

Inherited from:
Product
def productIterator: Iterator[Any]

Attributes

Inherited from:
Product

Inherited fields

lazy val freeVars: Set[String]

Cached set of free variable names; O(1) after the first access.

Cached set of free variable names; O(1) after the first access.

Attributes

Inherited from:
_Expression